Stability and Unidimensionality in Monster Metric Spaces
نویسنده
چکیده
This article investigates stability for monster metric spaces introduced in [ShUs837] without the additional assumtion of the language L being countable. We prove that any monster metric space which is categorical in any cardinality bigger than |L| is 0-stable in |L| and unidimensional. In particular, the result holds for uncountable continuous theories.
منابع مشابه
Model Theoretic Stability and Categoricity for Complete Metric Spaces Sh837
We deal with systematic development of stability for the context of approximate elementary submodels of a monster metric space, which is not far, but still very different from first order model theory. In particular we prove the analogue of Morley’s theorem for classes of complete metric spaces.
متن کاملStability of the quadratic functional equation in non-Archimedean L-fuzzy normed spaces
In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-Archimedean $mathcal{L}$-fuzzy normed spaces.
متن کاملExistence and uniqueness of the solution for a general system of operator equations in $b-$metric spaces endowed with a graph
The purpose of this paper is to present some coupled fixed point results on a metric space endowed with two $b$-metrics. We shall apply a fixed point theorem for an appropriate operator on the Cartesian product of the given spaces endowed with directed graphs. Data dependence, well-posedness and Ulam-Hyers stability are also studied. The results obtained here will be applied to prove the existe...
متن کاملDefinition of General Operator Space and The s-gap Metric for Measuring Robust Stability of Control Systems with Nonlinear Dynamics
In the recent decades, metrics have been introduced as mathematical tools to determine the robust stability of the closed loop control systems. However, the metrics drawback is their limited applications in the closed loop control systems with nonlinear dynamics. As a solution in the literature, applying the metric theories to the linearized models is suggested. In this paper, we show that usin...
متن کامل$C$-class and $F(psi,varphi)$-contractions on $M$-metric spaces
Partial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In 2014 Asadi and {it et al.} [New Extension of $p$-Metric Spaces with Some fixed point Results on $M$-metric paces, J. Ineq. Appl. 2014 (2014): 18] extend the Partial metric spaces to $M$-metric spaces. In this work, we introduce the class of $F(psi,varphi)$-contrac...
متن کامل